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Encoding of Naturalistic Optic Flow by a Population of Blowfly Motion-Sensitive NeuronsKarmeier, K.; Hateren, J.H. van; Kern, R.; Egelhaaf, M.

Published in:Journal of Neurophysiology

DOI:10.1152/jn.00023.2006

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Citation for published version (APA):Karmeier, K., Hateren, J. H. V., Kern, R., & Egelhaaf, M. (2006). Encoding of Naturalistic Optic Flow by aPopulation of Blowfly Motion-Sensitive Neurons. Journal of Neurophysiology, 96(3), 1602-1614.https://doi.org/10.1152/jn.00023.2006

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https://doi.org/10.1152/jn.00023.2006

Encoding of Naturalistic Optic Flow by a Population of BlowflyMotion-Sensitive Neurons

K. Karmeier,1 J. H. van Hateren,2 R. Kern,1 and M. Egelhaaf1

1Department of Neurobiology, Faculty for Biology, Bielefeld University; Bielefeld, Germany; and 2Department of Neurobiophysics,University of Groningen, Groningen, The Netherlands

Submitted 10 January 2006; accepted in final form 28 April 2006

Karmeier, K., J. H. van Hateren, R. Kern, and M. Egelhaaf.Encoding of naturalistic optic flow by a population of blowflymotion-sensitive neurons. J Neurophysiol 96: 1602–1614, 2006.First published May 10, 2006; doi:10.1152/jn.00023.2006. In sen-sory systems information is encoded by the activity of populations ofneurons. To analyze the coding properties of neuronal populationssensory stimuli have usually been used that were much simpler thanthose encountered in real life. It has been possible only recently tostimulate visual interneurons of the blowfly with naturalistic visualstimuli reconstructed from eye movements measured during freeflight. Therefore we now investigate with naturalistic optic flow thecoding properties of a small neuronal population of identified visualinterneurons in the blowfly, the so-called VS and HS neurons. Theseneurons are motion sensitive and directionally selective and areassumed to extract information about the animal’s self-motion fromoptic flow. We could show that neuronal responses of VS and HSneurons are mainly shaped by the characteristic dynamical propertiesof the fly’s saccadic flight and gaze strategy. Individual neuronsencode information about both the rotational and the translationalcomponents of the animal’s self-motion. Thus the information carriedby individual neurons is ambiguous. The ambiguities can be reducedby considering neuronal population activity. The joint responses ofdifferent subpopulations of VS and HS neurons can provide unam-biguous information about the three rotational and the three transla-tional components of the animal’s self-motion and also, indirectly,about the three-dimensional layout of the environment.

I N T R O D U C T I O N

Even single aspects of the world, such as the orientation ofcontours or the frequency of a tone, induce an activity patternspread over multiple neurons. A given environmental situation,such as the movements of an animal in its environment, isreflected in this neuronal population activity rather than in theresponses of single neurons. Population coding of sensoryinformation has been analyzed in many studies (e.g., Averbeckand Lee 2004; Deadwyler and Hampson 1997; Nirenberg andLatham 1998; Pouget et al. 2000). The sensory input an animalencounters in real life, however, may have much more complexproperties than the experimenter-defined stimuli usually usedin these studies (for review see Reinagel 2001).

We analyze the coding properties of a population of motion-sensitive visual interneurons in the blowfly with naturalisticstimuli generated actively by the animal during nearly unre-strained behavior. This neuronal population consists of twoclasses of neurons, the 10 VS (vertical system) neurons (Heng-

stenberg 1982; Hengstenberg et al. 1982; Krapp et al. 1998)and the three HS (horizontal system) neurons (Hausen1982a,b) whose response properties and function in visuallyguided behavior have been characterized in great detail (forreviews see Borst and Haag 2002; Egelhaaf et al. 2002, 2004).HS neurons are excited primarily by front-to-back motion andtheir receptive fields jointly cover one visual hemisphere. Thelatter is also true for VS neurons, which are most sensitive todownward motion within a vertical stripe of the visual field(Fig. 1A). Based on their receptive field properties (Krapp et al.1998, 2001) and their synaptic connections, all VS and HSneurons were proposed to act mainly as rotation sensors (Far-row et al. 2005; Haag and Borst 2001, 2004; Horstmann et al.2000; Krapp et al. 2001).

This view was challenged recently when two individualneurons, the HSE and the H1, were stimulated with the retinalimage motion encountered by freely flying flies (Boeddeker etal. 2005; Kern et al. 2005; van Hateren et al. 2005). Theseneurons could be demonstrated to make use of the saccadicflight strategy of freely flying flies, where most rotationalself-motion is squeezed into brief periods of high rotationvelocity, the saccades. Between saccades 1) the gaze is keptbasically straight (Schilstra and van Hateren 1999; van Haterenand Schilstra 1999) and 2) both neurons provide informationabout rotational and translational self-motion and thus indi-rectly about the three-dimensional (3D) structure of the envi-ronment (Kern et al. 2005; van Hateren et al. 2005). Thesestudies revealed that the coding properties of visual interneu-rons under natural stimulus conditions are not easily predict-able from results of studies using conventional experimenter-defined stimuli.

Here, we characterize for the first time almost the entirepopulation of VS and HS neurons, representing the majormotion-sensitive output neurons of the blowfly visual system,with naturalistic retinal image motion. We will demonstratethat all three rotational and translational self-motion compo-nents can be decoded from appropriately combined responsesof different VS and HS neurons, if the specific retinal imagemotion as actively generated by the fly in free-flight maneuversis taken into account.

M E T H O D S

Visual stimulation

The position and orientation of the head of blowflies (Calliphoravicina) flying in a cage of about 40 � 40 � 40 cm3 were recorded

Address for reprint requests and other correspondence: M. Egelhaaf, De-partment of Neurobiology, Faculty for Biology, Bielefeld University, Postfach10 01 31, D-33501 Bielefeld, Germany (E-mail: [email protected]).

The costs of publication of this article were defrayed in part by the paymentof page charges. The article must therefore be hereby marked “advertisement”in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.

J Neurophysiol 96: 1602–1614, 2006.First published May 10, 2006; doi:10.1152/jn.00023.2006.

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using magnetic fields driving search coils attached to the flies’head (Schilstra and van Hateren 1999; van Hateren and Schilstra1999). Because the compound eye is an integral part of the head,and the spatial coordinates of the head and the visual interior of thecage are known, we could use the head trajectory to reconstruct thevisual stimulus encountered by the fly during its flight (Fig. 1B;Lindemann et al. 2003). Reconstructions of 10 flights of 3.45-sduration each, originating from three different flies, were used inthe present measurements. Stimuli were presented using FliMax, aspecial-purpose panoramic stimulus device that generates imageframes at a frequency of 370 Hz (Lindemann et al. 2003). Each ofthe stimulus movies resulting from the reconstruction was accom-panied by a “no translation” variant (called “NT” below), recon-structed from the rotational movements (yaw, roll, and pitch) of theflies only, whereas their position was fixed to the center of thecage. During a recording we presented the normal and the mirroredversion of a movie, thus obtaining the response of the ipsilateralneuron and an approximated response of its contralateral counter-

part. This response will be referred to in the following as theresponse of the contralateral neuron.

Electrophysiology

Experiments were done on 1- to 2-day-old female blowflies (Cal-liphora vicina) bred in our laboratory stock. The dissection of theanimals for electrophysiological experiments followed standard pro-cedures described elsewhere (Warzecha et al. 1993). The flies’ eyeswere aligned with the stimulus device according to the symmetricaldeep pseudopupil (Franceschini 1975). Intracellular recordings fromVS and HS neurons in the right lobula plate (third visual neuropile)were made using borosilicate electrodes (GC100TF10, Clark Electro-medical) pulled on a Brown-Flaming puller (P-97, Sutter Instru-ments). Electrodes were filled with 1 M KCl and had resistancesbetween 20 and 40 M�. Recordings were carried out using standardelectrophysiology equipment. The data were low-pass filtered (cornerfrequency 2.4 kHz) and sampled at a rate of 4 kHz (I/O-card DT3001,

FIG. 1. Response characteristics of tangential neuronsduring stimulation with behaviorally generated optic flow.A: areas of main sensitivity to motion of fly tangentialneurons. VS (vertical system) neurons (shown for the leftside of the brain) are depolarized by downward motion, HS(horizontal system) neurons (shown for the right side of thebrain) by front-to-back motion in the most sensitive parts oftheir receptive fields. Maximum sensitivities of VS neuronsare distributed from the frontal (VS1) to the caudal part ofthe visual hemisphere (VS10). Sensitivity maximum of theHSS neuron is located in the ventral part of the visual field;the HSE neuron is most sensitive to motion in the equato-rial and the HSN neuron in the dorsal part of the visualfield. B: 1-s section of a fly’s trajectory (blue line) in a sideview in a cage of about 40 � 40 � 40 cm3. Position andorientation of the head are shown every 50 ms (red dots;green and magenta dots indicate respectively the start andend points of the flight sequence). C: self-motion of the flycan be decomposed into rotational (roll, pitch, yaw) andtranslational components (forward, sideward, upward/downward velocity) around/along the 3 cardinal head axes(frontal, transverse, vertical). D: head rotation (top) andtranslation velocity (bottom) during the flight segmentshown in B. Rotation and translation around/along thefrontal head axis (roll, forward velocity) in red, rotation andtranslation around/along the transverse head axis (pitch,sideward velocity) in blue, rotation and translation around/along the vertical head axis (yaw, upward/downward ve-locity) in black. Positive velocities denote leftward move-ments. As a visual aid for comparing the traces, black andgray dotted vertical lines indicate the beginning and end ofsaccades. E: average membrane potential of tangentialneurons. Top: ipsi- and contralateral VS6 neuron (meanover 4–5 traces). Bottom: ipsi- and contralateral HSS neu-ron recorded from another animal (mean over 3 traces).Response of the ipsilateral neurons was measured directly,and their response to appropriately mirrored versions of themovies provided an approximation of the response of thecontralateral neurons. Resting potential was set to zero(dotted horizontal line); neuronal response traces wereshifted back in time by 22.5 ms to account for responselatencies. Vertical lines as in D.

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Data Translation) using the VEE Pro 5.0 (Agilent Technologies) inconjunction with DT VPI (Data Translation) software. Experimentswere done at temperatures between 28 and 32°C. Such relatively hightemperatures closely approximate the fly’s head temperature duringflight (Stavenga et al. 1993). VS and HS neurons were identified bythe location of their receptive field, their preferred direction of motion,and their signal structure (Hausen 1982a,b; Hengstenberg 1982;Krapp et al. 1998).

Data analysis

SELF-MOTION COMPONENTS. We calculated the coherence betweenneuronal responses and each of the six parameters of self-motion.Three of the self-motion parameters are rotational: yaw, pitch, and rollvelocity; and the other three are translational: forward, sideward, andupward/downward velocity (Fig. 1C). The yaw velocity of the head isthe instantaneous angular velocity around a vertical axis through thehead and is obtained from the differential rotation matrix in thecoordinate system of the head (Schilstra and van Hateren 1999; vanHateren and Schilstra 1999). Pitch and roll are rotations aroundtransverse and frontal axes through the head, respectively. The for-ward, sideward, and upward/downward velocity of the head are thevelocity components along frontal, transverse, and vertical axesthrough the head, respectively. We found that typically only a few ofthese parameters gave coherences �0.1 for a particular type ofneuron.

COHERENCE CALCULATION. The coherence between a certain self-motion parameter of the fly (e.g., yaw velocity) and the neuronalresponse was calculated as �b

2(�) � � Psr(�) �2/[Pss(�)Prr(�)] (Haagand Borst 1998; Theunissen et al. 1996; van Hateren and Snippe2001), where Psr is the cross-spectral density of self-motion velocityand response, Pss is the power spectral density of the self-motionvelocity and Prr is that of the response, and � � 2�f, where f isfrequency. Spectra were calculated by periodogram averaging of 50%overlapping data segments, with each periodogram being the discreteFourier transform of a cos2-tapered zero-mean data segment of 256ms, extended by zero-padding to 512 ms. Results were not stronglydependent on segment length. Before segmentation, the response wasaligned with the stimulus by shifting it 22.5 ms backward in time, theapproximate latency under the experimental conditions. Results werenot strongly dependent on shift size. Segments from all flights (be-tween one and ten) used as stimulus for a particular neuron wereincluded in the periodogram averaging. Bias in the coherence estimateof each stimulus repetition was corrected by �2 � [n/(n � 1)�b

2] �1/(n � 1) (van Hateren and Snippe 2001; van Hateren et al. 2002),where n is the number of segments (n � 25–250 for the one to tenflights of the present experiments). Coherences were finally averagedover all stimulus repetitions.

COHERENCES WITH MORE THAN ONE PARAMETER. The coherencebetween the response and a second self-motion parameter was ob-tained by first conditioning the second parameter with the first (Bendatand Piersol 2000), i.e., s�2(�) � s2(�) � [P21(�)/P11(�)]s1(�), wheres1(�) is the first parameter (e.g., Fourier transform of yaw velocity)and s2(�) and s�2(�) are, respectively, the original and conditionedsecond parameters (e.g., Fourier transform of sideward velocity); P21

and P11 are cross- and power spectra of the second and first param-eters. Conditioning removes from s2 the second-order statistical de-pendency with s1. With three stimulus parameters (e.g., yaw, side-ward, and forward velocity; Fig. 3B), the conditioned third parameteris s�3 � s3 � (P32�/P2�2�)s�2 � (P31/P11)s1, where the dependency on �is omitted for simplicity of notation. This conditioning removes froms3 the second-order statistical dependency with both s1 and s�2. Wefound for the parameters used in this study that the order of evaluatingparameters does not significantly affect the coherences of eachparameter.

COHERENCE IN INTERSACCADIC INTERVALS. The above methodgives coherences for the entire response. These coherences may bestrongly dominated by the saccades because at least rotational self-motion parameters are much larger during saccades than betweensaccades. To focus on the stimulus–response relationship betweensaccades, we constructed masks m(t) for masking (i.e., zeroing) thesaccadic part of the stimulus and response (Kern et al. 2005; vanHateren et al. 2005). We then calculated the coherence between amasked self-motion parameter m(t)s(t) and the masked responsem(t)r(t), rather than between the self-motion parameter s(t) andresponse r(t) as above. Masks selecting intersaccadic segments wereobtained by first constructing masks ms(t) selecting saccades. A maskms(t) was obtained by giving it the value 1 in a region surroundingeach saccade, and zero elsewhere. Saccades were detected from peaks(�500°/s) in the total angular velocity of the head. The saccadicregions were made large enough to include all parts of both saccadicstimulus and corresponding response. Regions of saccades that wereclose together were merged to reduce boundary effects. Edges of themasks were tapered with a 12.5-ms cos2-taper to reduce spectralleakage biasing the coherence estimate at high frequencies. The maskused for selecting the intersaccadic segments, m(t), is then defined asm(t) � 1 � ms(t). Masked data consisted of gated (transmitted) dataintermitted with blocks of zeroes. Although the mask shapes thepower and cross-spectra of the masked data, this shaping occurs in asimilar way for all spectra in the numerator and denominator of thedefinition of coherence. Consequently, the mask by itself does notgenerate coherence for uncorrelated data, as was confirmed in controlcomputations with uncorrelated noise. The coherence of masked datainclude the zero blocks, however, and therefore should be regarded asbelonging to the entire masked signal, not to just its intersaccadic part.

COHERENCE RATE. For coherence functions a coherence rate (vanHateren and Snippe 2001; van Hateren et al. 2002) can be defined asRcoh � ��0

f0 log2 (1 � �2)df, where f is frequency and f0 represents afrequency sufficiently high such that the coherence has become zero(default 150 Hz in this study). The coherence rate is expressed in bit/sand can be considered as a biased information rate; it is equal toShannon’s information rate in the case of independent Gaussiansignals and noise. The coherence rate is used here as a convenient wayto assign a single number to the coherence function (van Hateren andSnippe 2001).

TUNING OF VS NEURONS. For an analysis of the tuning of VSneurons to the animal’s self-rotation, we did not use the coherences toself-motion around only the cardinal body axes. We projected theactual head rotation onto axes of varying elevation and azimuth(azimuth between �180 and 175°, elevation between �90 and 85°, 5° steps). We then calculated the coherence rate between the neuronalresponse and this projected head rotation (Fig. 2B). The rotational axis(i.e., azimuth and elevation) that gave the maximum coherence ratewas used as an estimate for the preferred rotation axis of the given VSneuron. For each neuron, such estimates were obtained for typicallyeight conditions (all combinations of normal and mirrored movie,original and NT stimulus version, and coherence of total or onlyintersaccadic response). The mean and SE of all estimates for aparticular neuron are shown in Fig. 2, C and D.

CALCULATION OF THE MEAN COHERENCE. Instead of showing alarge number of coherence functions for all groups of neurons and allconditions (normal and mirrored movie, original and NT stimulusversion, and coherence of total or only intersaccadic response), wecalculated a mean coherence by averaging over frequencies in a 10-Hzband around the frequency with maximum coherence. Because allneurons of a certain cell class (VS class or HS class) reveal a similarfrequency dependency for a particular self-motion component and aparticular stimulus condition (e.g., upward/downward translation orpreferred rotation for the original stimulus), we determined the posi-

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tion of the frequency band from the coherence averaged over allneurons belonging to that VS or HS class.

R E S U L T S

Flight description

The stimuli used in this study are reconstructed from theimage flow blowflies experienced during free flight in a cage.Figure 1B shows as an example a 1,000-ms section of a flighttrajectory. The head position (red dots) and orientation of thefly are shown every 50 ms. Flights can be described as a rapidsuccession of two phases, saccades and intersaccadic intervals.During “saccades” the fly shifts its gaze rapidly by fast headand body turns, whereas between saccades the gaze is keptrelatively stable. This gaze strategy becomes particularly ob-vious, if the fly’s self-rotation is decomposed into rotationsaround the three cardinal axes of the head (frontal, transverse,and vertical; Fig. 1, B and D, top). A saccade is characterizedby rotations around all three axes. As an aid to comparing thestimulus and response traces in the figure, the approximateposition of each saccade is marked by vertical lines at itsbeginning (black) and end (gray). The angular motions duringsaccades are dominated by rotations around the vertical axisthat reach velocities of up to a few thousand degrees per second(yaw; black). Rotations around the transverse (pitch; blue) andthe frontal axes (roll; red) are smaller and reach only about1,000°/s. Between saccades the rotation velocities of the headaround all three axes are by at least one order of magnitudesmaller and are typically �200°/s (van Hateren and Schilstra1999). In contrast to the rotational velocities, the time course ofthe translational velocity components is not structured in asimilar way by the saccades. Rather, the translation velocitiesvary relatively smoothly and show no consistent changes

during the saccades [Fig. 1D, bottom; forward (red), sideward(blue), and upward/downward (black) velocities]. The forwardvelocity for the flight segment shown in Fig. 1B varies between0 and 0.5 m/s. In other sections of the flights used it reaches �1m/s (Schilstra and van Hateren 1999). The sideward andupward/downward velocities fluctuate around 0 m/s. For allflights, both the sideward and the upward/downward motionreach maximum velocities of about 0.5 m/s.

Responses of tangential neurons to naturalistic optic flow

Figure 1E shows the time course of averaged responses of anipsilateral VS6 neuron (black line, top) and of an HSS neuron(black line, bottom) as well as the responses inferred for therespective contralateral neurons (gray). The responses wererecorded from a blowfly watching the movie reconstructedfrom the flight shown in Fig. 1B. Both types of neuronsrespond with graded changes of their membrane potential tothe naturalistic optic flow. The activity of both VS6 neuronsmodulates considerably around the resting potential (set tozero). For large parts of the flight the membrane potentialmodulations of the ipsi- and contralateral VS6 neuron appear tobe in counterphase. It is hard to relate the responses to anysingle self-motion parameter. In particular, pronounced de- andhyperpolarizations are induced not only by the high rotationvelocities during saccades but also in the intersaccadic inter-vals. Because the most obvious changes of translation velocityappear to occur on a slower timescale than most rotationalvelocity changes, the membrane potential changes, in particu-lar between saccades, may be also related to the translationalflow component. At first sight, these results on the VS6 neuronappear to be in contrast to results obtained with simple exper-imenter-defined stimuli, where this neuron was concluded to be

FIG. 2. Classification of VS neurons and determinationof the respective preferred rotation axis. A: receptive fieldas determined by the difference between the neuronalresponses to an up- and downward moving dot for a VS1and a VS6 neuron. Difference responses are plotted as afunction of the stimulus positions along the azimuth.Gaussian functions are fitted to the measured data of the 2neurons. Arrows pointing at the x-axis denote the maxi-mum of the fits and can be regarded as the sensitivitymaximum of the respective neurons. B: tuning curve of theVS6 neuron to rotation obtained from the coherence rate.Inset: coherence functions between the VS6 neuron’s re-sponse and the roll and pitch velocity. Coherence rate wascalculated from the coherence function over a frequencyrange from 1 to 150 Hz. To obtain the tuning curve, thecoherence rate was calculated for head rotations aroundaxes in a 2-D grid. Azimuth between �180 (roll-axis) and175°, elevation between �90 and 85° (5° steps). Azimuthvalue of �90/90° corresponds to the pitch axis. C: azimuthand elevation of the average preferred rotation axes for allVS neurons recorded in the experiments. An average axisand corresponding SE were calculated by weighting theaxis for each stimulus condition, obtained from the peak ofa tuning curve as presented in B, with the coherence rate atthe respective peak. D: preferred rotation axes as a functionof receptive fields’ sensitivity maxima calculated as shownin A (mean and SE). Linear regression line fitted to the datahas a slope of �1.1.



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most sensitive to downward motion in the lateral visual fieldand considered as a detector for roll rotations (Fig. 1C;Karmeier et al. 2003, 2005; Krapp et al. 1998).

Similar conclusions can be drawn for HSS neurons (Fig. 1E,bottom). There is no clear and simple relationship between themembrane potential fluctuations evoked by naturalistic opticflow and any single self-motion parameter. Both HSS neuronsare depolarized with respect to the resting potential for most ofthe time during the flight. Their responses appear to be stronglyaffected by those saccadic turns that lead to image displace-ments in the antipreferred direction of the neuron. During thoserotations the neuron becomes hyperpolarized. Again, thesefindings obtained with naturalistic optic flow cannot easily beinferred from results and conclusions based on simple experi-menter-defined stimuli. Here, HSS neurons were found to bedepolarized by front-to-back motion (Fig. 1A) and inhibited byback-to-front motion. They are responsive to rotations of theanimal around a vertical axis, but, additionally, they respond totranslational optic flow occurring during forward and sidewardmotion of the animal (Hausen 1982b; Krapp et al. 2001).

Responses of similar complexity are obtained for all otherVS and HS neurons that were tested. Because it is hardly

possible to infer which aspects of self-motion are encoded byVS and HS neurons under natural conditions just by looking atthe complex neuronal responses, the data will be analyzed in aquantitative way.

VS neurons

RECEPTIVE FIELDS AND PREFERRED AXES OF ROTATION. Like theVS6 neuron (Fig. 1E) all VS neurons have been suggested, onthe basis of experiments with simple motion stimuli, to analyzeoptic flow resulting from rotations of the animal’s head arounda specific axis located in the horizontal plane (Krapp et al.1998). The preference of a given VS neuron for a specificrotation axis is mediated by the distribution of local directionalmotion sensitivities within its receptive field (Krapp et al.1998). The receptive fields of VS neurons from one half of thebrain cover large parts of the corresponding visual hemisphere,but the maximum sensitivities to downward motion are distrib-uted from the frontal (VS1) to the caudal part of the visualhemisphere (VS10) (Fig. 1A; Farrow et al. 2005; Haag andBorst 2004; Hengstenberg et al. 1982; Krapp et al. 1998). Wetook advantage of the different spatial locations of the sensi-

FIG. 3. Coherences between responses of tangential neurons and rotational or translational velocities. A: mean and SE of the coherence between the response(entire flight) of each VS4-6 neuron and the rotational velocity around its preferred rotation axis, and coherence with upward/downward velocity. Preferredrotation axis was obtained from the tuning curve calculated from coherence rates (cf. Fig. 2B). Horizontal bars in A–D denote the integration windows used tocalculate the mean coherences shown in E and F. For clarity, error bars are shown for only every other data point. B: coherence between the HSS neuron responseand a preferred axis rotation, sideward and forward translation for the entire flight. We assumed the yaw axis as the preferred rotation axis of HS neurons. C:as in A, for the response in the periods between the saccades. D: coherence between the HSS neuron response and a preferred rotation, sideward and forwardtranslation for the periods between the saccades. Coherences in C and D were calculated by masking out the saccadic part of the stimulus and the neuronalresponse (cf. METHODS). E: mean coherences of all VS neuron types for a preferred axis rotation and an upward/downward translation for the entire flight andbetween the saccades. Frequencies were averaged over a frequency band of 10 Hz, centered near the maximum coherence for each condition. F: mean coherencesof all HS neuron types for preferred rotation (yaw), sideward translation, and forward translation for the entire flight and between the saccades. All coherencesand mean coherences are averages over the right and left neurons (VS1, 5 neurons; VS2-3, 4 neurons; VS4-6, 8 neurons; VS7, 1 neuron; HSN, 9 neurons; HSE,8 neurons; HSS, 9 neurons). Error bars show SE.



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tivity maxima when identifying VS neurons. We stimulatedeach recorded neuron with a dot moving up- and downward atdifferent azimuthal positions from �15° at the contralateralside to 120° at the ipsilateral side (resolution 15°). A 0° anglecorresponds to the frontal midline of the visual field; positiveand negative angles refer to angular positions in the right andleft visual field, respectively. Figure 2A shows the resultingspatial sensitivity distribution of a VS1 and a VS6 neuron, asdetermined by the difference between the responses to down-and upward motion of the dot. Both neurons show a clearsensitivity maximum, but respond to motion stimuli over abroad range of stimulus positions. We fitted a Gaussian func-tion to the measured data and took the maximum of the fit asthe sensitivity maximum of the neuron (arrows in Fig. 2A). Thesensitivity maximum of the VS1 neuron was found at anazimuth close to 0°, the maximum of the VS6 neuron close to90°. The sensitivity maxima of VS2 to VS5 are locatedbetween the maxima of VS1 and VS6 (Fig. 2D).

To determine the preferred rotation axes of the different VSneurons when stimulated with naturalistic optic flow, we cal-culated for each neuron the coherence rate between the neuro-nal responses and rotations around axes of varying elevationand azimuth (cf. METHODS and Fig. 2B). The inset in Fig. 2Bshows, as an example, the coherence between a VS6 neuron’sresponse and rotations around two rotation axes (roll axis:azimuth 0/180° and elevation 0°, corresponding to the headfrontal axis; pitch axis: azimuth �90/90° and elevation 0°,corresponding to the head transverse axis). The coherencequantifies, as a function of frequency, the similarity of aself-motion parameter (here either roll or pitch) and the self-motion parameter predicted from the response by the optimallinear filter. The coherence varies between zero (i.e., at fre-quencies where the parameters are not linearly related) and one(i.e., perfect prediction; see METHODS). The coherence rate isobtained by integrating over the coherence function (see METH-ODS) and is a convenient way to collapse the coherence functioninto a single number (van Hateren and Snippe 2001). Figure 2Bshows the coherence rates between the response of a singleVS6 neuron and head rotations around a range of rotation axescovering the entire visual sphere. As can also be inferred fromthe coherence functions in the inset, the coherence rate washigh for rotations around the roll axis, but low for rotationsaround the pitch axis. The rotation axis (i.e., with azimuth andelevation given at 5° resolution) that gave the maximumcoherence rate was used as an estimate for the preferredrotation axis of the VS6 neuron. These estimates were obtainedfor typically eight stimulus conditions (all combinations ofnormal and mirrored movies, original and NT stimulus version,and coherence of total or only intersaccadic response). Theestimates of the preferred rotation axes of a certain neuronwere averaged and the SE provided a measure of the error inthe average. We show in Fig. 2C the azimuth and elevation ofthe preferred rotation axes for all VS neurons recorded in theexperiments. The preferred rotation axes are distributed withinan azimuthal range of 110° (between �25 and 85°). Theelevation varies little and is generally close to 0° (i.e., thehorizontal plane). It should be noted that the preferred axes ofrotation as determined on the basis of naturalistic optic flow arevery similar to those predicted from experiments using exper-imenter-defined, local motion stimuli (Krapp et al. 1998,2001).

Interestingly, the preferred axes of rotation of the differentVS neurons are related to the location of their receptive fields,i.e., the region in the visual field where they are most sensitiveto motion. The position of the sensitivity maximum of a VSneuron measured with the dot stimulus is almost orthogonal tothe corresponding preferred rotation axis. The two character-istics show a linear relationship (Fig. 2D; slope of regressionline �1.1).

For the following analysis, we classified the recorded VSneurons on the basis of their response characteristics and theirpreferred axes of rotation (Fig. 2C). The VS1 neuron has verydistinctive response properties and could thus be classifiedunambiguously (Krapp et al. 1998). The preferred rotation axesof all recorded VS1 neurons were located in a small azimuthalrange between 75 and 85° (five neurons analyzed). A secondgroup of neurons had their preferred rotation axes located in anazimuthal range between 46 and 63° and could be distin-guished unambiguously from VS1 neurons. We pooled theseneurons in the group of VS2-3 neurons because VS2 and VS3neurons have virtually identical receptive fields and preferreddirections (Krapp et al. 1998) and could also not be distin-guished by the orientation of their preferred axes (four neuronsbelonging to this group were analyzed in detail). AlthoughVS4, VS5, and VS6 neurons show slightly different receptive-field structures (Krapp et al. 1998), they could not be distin-guished unambiguously on the basis of the identification stim-uli used here. Because the preferred rotation axes of this groupof neurons very clearly differ from those of the VS2-3 neurons,they were pooled in the group VS4-6 (eight neurons of thisgroup were analyzed in detail). A single neuron we recordedfrom had its preferred rotation axis at an azimuthal position of�25°. Because this neuron clearly differed in its sensitivitymaximum as well as in its preferred rotation axis from theneurons of the VS4-6 group, we classified it as a VS7 neuron.Neurons with more caudally oriented receptive fields could notbe stimulated adequately with the stimulus device. It should benoted that the conclusions drawn in this study do not depend onthe classification scheme used here. Qualitatively the sameconclusions can be drawn when all neurons are treatedseparately.

COHERENCE FOR NATURALISTIC STIMULI. To determine howwell different self-motion parameters are represented by thetime-dependent responses of individual VS neurons to natural-istic optic flow, we calculated the coherences for rotationsaround their respective preferred axis and for upward/down-ward translation. As an example, Fig. 3, A and C shows themean coherences determined for neurons of the VS4-6 group.If the entire flight is taken into account (Fig. 3A), the coherencebetween the neuronal responses and the rotation around thepreferred axis (i.e., approximately the roll axis; see Fig. 2C) is�0.1 between 5 and 35 Hz. Surprisingly, the coherence for theupward/downward translation is small, although all VS neu-rons respond well to constant velocity up- and downwardmotion (Hengstenberg 1982; Hengstenberg et al. 1982;Karmeier et al. 2003). This difference is understandable be-cause during saccades the rotational velocities are usuallymuch larger than the angular velocities resulting from upward/downward translation and thus dominate the overall optic flow.The situation is different for the intersaccadic intervals. Thuswe calculated the coherences for rotations around the preferred



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axes and for upward/downward translation separately betweensaccades (Fig. 3C). The coherences for the intersaccadic ve-locities are higher and �0.1 between 1 and 35 Hz for bothself-motion parameters. Thus it appears, in accordance withprevious experiments done with experimenter-defined opticflow (Karmeier et al. 2003), that individual neurons of theVS4-6 group do not provide the information to easily distin-guish between roll and upward/downward translation.

In Fig. 3E we compare for all groups of VS neurons thecoherences for the preferred axes of rotation (cf. Fig. 2C) andfor upward/downward translation. To combine all data in asingle panel, we calculated the mean coherence by averagingthe coherence functions over frequencies in a 10-Hz bandaround the frequency with maximum coherence (e.g., horizon-tal bars in Fig. 3, A and C). The mean coherences for rotationsaround the preferred axis and for upward/downward translationcalculated for the entire flight are in the same range for allgroups of VS neurons. Coherences �0.1 are obtained only forrotations. The coherences for the upward/downward translationwere much smaller. In contrast to coherences for the entireflight, the coherences calculated for upward/downward trans-lation in the intersaccadic intervals are �0.1 for all neurongroups. The coherences for the intersaccadic rotation velocitiesaround the preferred axes differ between groups of VS neu-rons: The coherence for the intersaccadic rotation velocity ishigher than the coherence for the entire flight for neurons of theVS4-6 and VS7 groups, although it decreases for neurons ofthe VS2-3 group and becomes almost negligible for VS1neurons. This feature may be attributable to interference be-tween the responses to rotation and translation.

This hypothesis is corroborated by results obtained with theNT stimulus (no translation; see METHODS), which allowed us tostudy the coding properties of VS neurons for rotations alone,

i.e., without simultaneous translational movements. The coher-ence function for the entire flights between preferred axisrotations and the neuronal responses shows similar values andfrequency dependencies as the coherences of the original flightwith simultaneous translations (compare Fig. 4, A and C to Fig.3, A, C, and E). However, the coherences for the intersaccadicrotation velocities are higher than the coherences for rotation ofthe entire flight for all groups of VS neurons (Fig. 4C) and donot decrease at the lowest frequencies (Fig. 4A). The highercoherences between saccades are likely to be a consequence ofthe limited range in which the visual motion detection systemencodes velocity linearly (Egelhaaf and Reichardt 1987; Haagand Borst 1997). We conclude from the comparison of thecoherences obtained for the original and the NT flights thatbetween saccades of normal flights, VS neurons carry infor-mation not only about rotation but also about upward/down-ward translation.

HS neurons

RECEPTIVE FIELDS AND THE “CLASSICAL VIEW”. Like the HSSneuron shown in Fig. 1D, the other two types of HS neuronsare also depolarized by front-to-back motion in the ipsilateralvisual field, and all HS neurons were previously regarded asdetectors of yaw rotations. The locations of the receptive fieldsdiffer between the three HS neurons. Whereas the sensitivitymaximum of the HSS neuron is located in the ventral part ofthe visual field, the HSE neuron is most sensitive to motion inthe equatorial and the HSN neuron in the dorsal part of thevisual field. In addition to their main motion input in theipsilateral visual field, HSN and HSE receive contralateralinput from heterolateral connecting elements, in particular H1and H2, that are sensitive to back-to-front motion (Haag and

FIG. 4. Mean coherences between tangential neurons’ re-sponses and the “no translation” stimulus (NT). A: meancoherence of a neuron from the VS4-6 group neurons calcu-lated for the rotation around the preferred axis for the entireNT flight and between the saccades (mean and SE). Horizontalbars in A and B denote the frequency range used to calculatethe mean coherences shown in C and D. B: coherence betweenthe HSN neurons’ responses and yaw rotation for the entireflight and between the saccades. C: mean coherences for 3groups of VS neurons calculated for the preferred rotation axisfor the entire stimulus and between the saccades. D: meancoherences for the 3 HS neuron types calculated for yawrotation for the entire NT stimulus and between the saccades.Mean coherences are averages over the right and left neuron(VS1, 5 neurons; VS2-3, 3 neurons; VS4-6, 4 neurons; HSN,8 neurons; HSE, 2 neurons; HSS, 1 neuron). Error bars showSE.



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Borst 2001; Hausen 1976, 1981, 1982b; Horstmann et al. 2000;Krapp et al. 2001). In an approach using naturalistic optic flow,Kern et al. (2005) concluded that the HSE neuron rather thanprimarily encoding yaw rotations of the animal also encodesinformation about sideward translation in the intersaccadicintervals. Here we show data for all three HS neurons. On thewhole, the results for all HS neurons are similar, although thereare characteristic differences that may be related to theirdifferent receptive locations and the presence or absence ofcontralateral input.

COHERENCE FOR NATURALISTIC STIMULI. For HS neurons wecalculated the coherences between neuronal responses and theyaw rotation and those translations that can be expected toactivate HS neurons, i.e., sideward and forward translation.Figure 3, B and D shows, as an example, the coherencefunctions calculated for HSS neurons. For the entire flight onlythe coherence of yaw velocity shows values �0.1 (between 1and 15 Hz), whereas the coherences for both forward andsideward velocity are small (Fig. 3B). The coherence of theintersaccadic yaw and the sideward velocity are higher andhave their maxima in adjacent frequency bands: Whereas thecoherence of the intersaccadic yaw velocity and the neuronalresponse is �0.1 between about 20 and 60 Hz, the coherenceof sideward velocity is high only at low frequencies �20 Hz(Fig. 3D). The mean coherences for all HS neurons, averagedover the frequency bands indicated by the horizontal bars inFig. 3, B and D, are given in Fig. 3F.

For all HS neurons the intersaccadic yaw and sidewardvelocities were coded in different frequency bands as shownfor the HSS neuron in Fig. 3D. HS neurons might make use ofthis difference to provide information on both optic flowcomponents in adjacent (and thus separable) frequency bands(Kern et al. 2005). A comparable separation of informationabout rotational and translational components of self-motion isnot possible for VS neurons, where rotation and translation arecoded in similar frequency bands for both the entire flight andbetween the saccades (Fig. 3, A and C). Although the absolutecoherence values obtained for the different HS neurons varied,possibly as a consequence of different average stimulus con-trast in their receptive fields, they exhibited a similar relation-ship between the values obtained for the different self-motionparameters. In particular, the coherences between the neuronalresponses and forward velocity were much smaller than thosefor sideward velocity.

If the translational components are eliminated from the opticflow, simulating pure rotations of the fly (NT-stimuli), itbecomes obvious that, as in VS neurons, the translationalcomponent of self-motion had a substantial impact on theneuronal responses. For the entire NT flight the yaw coherencewas larger than that for the original flight with translationalcomponents, but showed a similar frequency dependency (Fig.4B, black line). If evaluated for the intersaccadic intervals thecoherence function of the NT flights was also high in thelow-frequency range, in contrast to the original flight (see alsoKern et al. 2005). Similar to the VS neurons, all classes of HSneurons have a higher coherence between rotation and re-sponses in intersaccadic intervals than for the entire flight (Fig.4D).

Population coding

The coherence analysis of the responses of VS and HSneurons demonstrates that responses of single neurons carrysignificant, but partly ambiguous, information about self-mo-tion. This gives rise to the question to what degree the com-bination of signals from different neurons can disambiguate thedecoding. Two recent studies already demonstrated this im-provement for tangential neurons: Kern et al. (2005) demon-strated that information of different parameters of self-motioncan be separated by combining the responses of the ipsi- andcontralateral HSE neurons. Karmeier et al. (2005) showed thatthe axis of self-rotation can be extracted with high accuracyfrom the population response of all VS neurons. As a firstapproach to analyzing population coding of naturalistic opticflow, we investigate linear combinations of neuronal signalsand calculate the coherences with rotations around and trans-lations along the three cardinal head axes (roll, pitch, and yaw;forward, sideward, and upward/downward). It should be notedthat our analysis has limitations in addition to investigatinglinear combinations and focusing on orthogonal, cardinal axes.First, we did not record simultaneously from the variousneurons, which implies that we cannot infer on possible cor-relations between the noise in the different neurons. Second,the neurons are generally recorded in different animals, whichimplies that possible correlations between the processing prop-erties of different neurons in the same animal (e.g., throughparticularities of their common input elements) cannot bedetected as well. For technical reasons, however, simulta-neously recording from more than one of the HS and VSneurons with sufficient quality for a coherence analysis isextremely difficult. The approach we take here should there-fore be considered as a first albeit feasible approach to thequestion how naturalistic, behaviorally generated optic flow isrepresented in the blowfly’s brain.

CODING OF SELF-MOTION BY SUBPOPULATIONS OF VS NEURONS.

The responses of individual VS neurons carry informationabout different rotation axes as well as about upward/down-ward velocity. We analyzed whether the specificity to self-rotation is enhanced by subtracting the responses of two sets ofVS neurons from opposite halves of the brain having the samepreferred rotation axis but opposite preferred rotation direc-tions. In Fig. 5A we show the coherence function calculatedbetween the intersaccadic roll velocity and a composite re-sponse. This composite response was obtained by subtractingthe summated response of four ipsilateral neurons (three re-sponses from three representative neurons of the VS4-6 groupand one response from a VS7 neuron) from the summated fourresponses of the corresponding contralateral neurons. Thecoherence function was �0.1 between 1 and 50 Hz and showsa frequency dependency similar to that of the coherence cal-culated for the responses of individual VS4-6 neurons (cf. Fig.3C). The coherence values, however, are larger than the valuescalculated for individual VS4-6 neurons. This is because moreneuronal responses are incorporated in the analysis, whichshould increase the signal-to-noise ratio, and thus the coher-ence. The difference signal of a single VS4-6 neuron pair givessimilar, but slightly lower coherences. This finding indicatesthat the exact grouping of VS neurons is not important withrespect to the encoding of roll rotation. Because there isvirtually no coherence between the difference signals and



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upward/downward velocity (Fig. 5A), taking the differencebetween VS neurons with opposite rotation sensitivities in-creases the specificity for rotational self-motion.

We could not obtain responses of VS10 neurons because thestimulus device does not allow us to stimulate neurons of thisgroup that have their receptive fields in the rear part of thevisual field. Because VS10 neurons were predicted on the basisof experimenter-defined stimuli to have approximately thesame rotation axis as that of VS1 neurons but opposite pre-ferred directions (Krapp et al. 1998), it is reasonable to hy-pothesize that subtracting the sum of the ipsi- and contralateralVS1 responses from the sum of the ipsi- and contralateralVS10 responses would yield a sizable and specific coherencewith pitch.

Because all VS neurons respond to some extent to upward/downward translation, we tested whether the specificity for thistranslational component could be enhanced by an additivecombination of all VS neurons. The coherence between theneuronal responses and upward/downward velocity was calcu-lated from the signal obtained by summating the responses ofrepresentative neurons from all VS groups recorded in theexperiments (seven neuronal responses from the ipsilateral sideand seven neuronal responses from the contralateral side).Figure 5B shows that the coherence to upward/downwardvelocity was enhanced compared with single-neuron coher-ences by taking the responses of many VS neurons intoaccount. The intersaccadic coherence to upward/downwardvelocity was �0.1 between 1 and 55 Hz and the peak coher-ence is considerably higher than that for individual VS neurons(between 0.1 and 0.2; see Fig. 3E). The coherences between thesummated responses of VS neurons and different rotationalself-motion components are negligible (Fig. 5B). Thus adding

the responses of a population of VS neurons increases thespecificity for upward/downward translation.

POPULATION CODING IN HS NEURONS. The responses of all HSneurons carry information about yaw and sideward velocity. Ina recent study, Kern et al. (2005) showed that the specificity ofintersaccadic responses to translational self-motion compo-nents is enhanced by combining the responses of HSE neuronsfrom both halves of the brain. Here we show that combiningthe responses of the ipsi- and contralateral neuron enhances thespecificity of all HS neurons.

The coherence calculated between the summated signals ofipsi- and contralateral HSS neurons and forward translation isgenerally higher than the coherence calculated for the signal ofindividual HSS neurons (compare Figs. 5C and 3F). The valueswere �0.1 between 1 and 35 Hz. The coherence with yaw andsideward velocity (Fig. 5C, inset) is negligible in all three HSneurons, demonstrating that summation increases the specific-ity of these neurons to a single parameter of optic flow. Thecoherence with forward velocity was, of all HS neurons,highest for the HSS neuron (Fig. 5C, inset), which may beexplained by both the absence of contralateral input to the HSSneuron and its sensitivity maximum in the ventral part of thevisual field. The difference between the responses of corre-sponding ipsi- and contralateral HS neurons enhances thecoherence for sideward and yaw velocities (Fig. 5D) andmakes the coherence with forward velocity negligible (Fig. 5D,inset). As for the coherences calculated from the response ofindividual HS neurons (cf. Fig. 3D), information about side-ward and yaw velocities is coded in adjacent frequency bands.The coherence for the difference response is larger for all typesof HS neurons than the values calculated for individual HSneurons (cf. Fig. 5D, inset, and Fig. 3F).

FIG. 5. Population coding of self-motion: coherences be-tween cardinal self-motion components and the populationresponse that leads to the highest coherence. A: coherencebetween intersaccadic roll rotation and a composite responseobtained by subtracting the summated response of ipsilateralVS4-7 neurons from the summated 4 responses of the corre-sponding contralateral neurons (4 neuron pairs). Coherencebetween intersaccadic upward/downward velocity and thecomposite response is negligible. B: coherence between in-tersaccadic upward/downward velocity and the sum over 7representative ipsilateral responses and the 7 correspondingcontralateral responses from VS1-7 neurons (7 neuron pairs).Coherence between intersaccadic roll velocity and the sum-mated response of ipsi- and contralateral VS1-7 neurons isnegligible. C: coherence between the summated responses ofthe left and right HSS neuron and the intersaccadic forwardvelocity (average and SE of 3 HSS neurons). Inset: meancoherences of the summated response of the left and rightneurons for all HS neurons (HSN, 9 neurons; HSE, 7 neurons;HSS, 3 neurons). Coherence was averaged over a 10-Hzwindow, centered near the maximum coherence. Coherencesbetween the summated responses of the left and right HSneurons and yaw and sideward velocity is negligible for all 3HS types. D: difference signal between the left and right HSSneurons produces high coherences with both intersaccadicyaw and sideward velocity (average of 3 HSS neurons). Inset:mean coherences of the difference signal for all HS neurons(HSN, 9 neurons; HSE, 7 neurons; HSS, 3 neurons). Coher-ences were averaged over 10-Hz windows. Coherence be-tween the difference response of all 3 HS neuron types andforward velocity is negligible. All coherences were calculatedfor the intersaccadic intervals.



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D I S C U S S I O N

Neuronal coding of visual motion has often been analyzedby characterizing single neurons with simple, experimenter-defined motion stimuli. This approach, however, is known tobe artificial: The characteristic temporal structure of the visualinput an animal experiences during unrestrained behavior dif-fers dramatically from the experimenter-defined motion stimuliused in earlier studies, whether it is constant velocity stimuli orwhite-noise velocity fluctuations (e.g., David et al. 2004; Kernet al. 2005; van Hateren et al. 2005; Vinje and Gallant 2002).Furthermore, it is known that information is conveyed byneuronal populations rather than by single neurons (e.g., Fitz-patrick et al. 1997; Georgopoulos et al. 1986; Groh 2000; Leeet al. 1998; Nicolelis et al. 1998; Theunissen and Miller 1991;Zhang et al. 1998). Therefore the aim of this study was toanalyze how self-motion is encoded by a population of blowflyvisual interneurons stimulated with naturalistic optic flow asgenerated during free-flight behavior. We could demonstratethat by exploiting the specific dynamics of natural optic flow;the population response provides information about all sixdegrees of freedom of self-motion.

The responses of individual sensory neurons are usuallyhighly ambiguous with respect to different stimulus parame-ters. This is also true for VS and HS neurons (Hausen 1982a,b;Hengstenberg 1982; Hengstenberg et al. 1982). Part of theseambiguities can be reduced when the neurons are stimulatedwith moving patterns that come close to natural scenes withregard to their statistical properties, i.e., which are composed ofa broad range of spatial frequency components and contrasts(Dror et al. 2001). The results of Dror et al. (2001) arecorroborated by the finding that during stimulation with natu-ralistic optic flow even large differences in the textural prop-erties of the scene have little effect on the responses of flymotion-sensitive neurons. Rather, the neuronal responses aremainly shaped by the characteristic dynamical properties of thenaturalistic optic flow (Boeddeker et al. 2005; Kern et al. 2005;Lindemann et al. 2005; van Hateren et al. 2005).

The specific dynamical properties of naturalistic optic floware the consequence of a saccadic flight and gaze strategy ofblowflies (Schilstra and van Hateren 1999; van Hateren andSchilstra 1999): Brief periods dominated by high rotationvelocities, the saccades, are followed by periods characterizedby almost stable gaze and thus much smaller rotational veloc-ities. This aspect of the gaze strategy of blowflies is reminis-cent of the saccadic eye movements of primates where theretinal image is stabilized by a pattern of fixations with inter-spersed fast saccades that shift the gaze direction to objects ofinterest (e.g., Becker 1992; Carpenter 1988). If blowflies aremoving in a textured environment containing nearby objects,the optic flow in the intersaccadic intervals constitutes signif-icant translational components and thus contains informationabout the spatial layout of the environment.

The relationship between the complex time-dependent re-sponses of the analyzed HS and VS neurons and the differentself-motion parameters is much more obvious only if theresponses during the intersaccadic intervals are taken intoaccount. If the entire flight is taken into account the responsesevoked by the rotational self-motion components dominatethose evoked by translational self-motion components and onlythe coherences for the rotational velocities are �0.1. If, in

contrast, only the responses during the intersaccadic intervalsare evaluated, the coherences to both the rotational and thetranslational components of optic flow reveal values �0.1.Therefore the blowfly’s saccadic flight and gaze strategy can beinterpreted as a means to separate actively rotational andtranslational optic flow components and thus facilitate thecomputation of behaviorally relevant information.

The computations that were used here to separate the sac-cadic and intersaccadic parts of the neuronal responses are usedonly for analytical purposes and not as a model of the neuralprocessing. The nervous system is likely to use differentstrategies. One possible strategy would be to suppress ormodify the neuronal response during saccades as has beenshown for the saccadic system of primates (e.g., Bair andO’Keefe 1998; Burr 2004; Thiele et al. 2002), implicatingsignals derived from the saccadic control system. In blowflies,this kind of top-down modification of the neuronal represen-tations of optic flow is apparently absent in VS and HS neuronsbecause their responses to naturalistic optic flow appear to beexclusively driven by the visual stimulus. This is concludedfrom the close similarity between the responses of HS neuronsand the output of a model of computational mechanismsimplemented by the neuronal circuits in the blowfly motionvision pathway (Lindemann et al. 2005). Nonetheless, it isconceivable that top-down signals play a decisive role inseparating the neuronal representation of natural optic flow intoits saccadic and intersaccadic components at some later pro-cessing stage.

Although the dynamics of naturalistic optic flow shape theresponses of VS and HS neurons, the responses of individualneurons are still ambiguous. Each VS neuron, for example,responds best to rotations about one axis located approximatelyin the equatorial plane of the head. Additionally each neuronrepresents information about upward/downward translationduring the intersaccadic intervals. Similarly, in the intersac-cadic intervals HS neurons provide information about yawrotations, sideward translation, and, to some extent, forwardtranslation. These ambiguities can be dramatically reduced byconsidering neuronal population activity. As predicted theoret-ically (e.g., Dahmen et al. 2000), the specificity for a particularaxis of self-rotation of the animal can be enhanced by asubtractive combination of pairs of neurons with differentpreferred rotation axes. Subtraction of the outputs of hetero-lateral VS4-6 and VS7 neurons increases the specificity forrotations around the roll axis (Fig. 6A). Accordingly, specificrepresentations of yaw rotations are obtained in a separablefrequency band (see following text) by subtraction of theresponses of ipsi- and contralateral HS neurons (Fig. 6B).Concerning the encoding of pitch rotations we can currentlypropose only a hypothesis because the probably involved VS10neuron cannot be stimulated adequately by our visual stimula-tor. The only data available on the VS10 neuron are thosebased on simple experimenter-defined stimuli (Krapp et al.1998). The measured preferred rotation axis of the VS1 and thepredicted axis of the VS10 neuron correspond to the pitch axis,although with opposite directions. Just as the subtractive com-bination of the heterolateral VS4-6 and VS7 neurons enhancesthe specificity for rotations around the roll axis, the specificityfor pitch rotation should be enhanced by subtracting the signalsof VS1 and VS10 neurons (Fig. 6C).



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A specific representation of upward/downward translation isobtained by adding the responses of all VS neurons in bothhalves of the brain (Fig. 6D). In a similar way, the addition ofthe responses of heterolateral HS neurons isolates the informa-tion carried about forward translation (Fig. 6E). Interestingly,the specificity of the summated responses for forward transla-tion decreases from the HSS by the HSE to the HSN neuron.This gradient may be explained by the fact that the HSS neuronhas its sensitivity maximum in the ventral part of the visualfield, which is well stimulated during forward motion. It mayalso be related to the different input organization of the HSSneuron compared with the HSE and HSN neurons. In contrastto the latter neurons, the HSS neuron does not receive inputfrom the contralateral eye (Hausen 1982a,b; Krapp et al. 2001).Recovering information about sideward translation from natu-ralistic optic flow appears, at first sight, to be more compli-cated. Sideward translation can be recovered by subtracting theoutput signals of the corresponding HS neurons from bothhalves of the brain (Fig. 6F). However, this difference signalalso provides information about yaw rotation (see above).Nonetheless, as was concluded in a previous study (Kern et al.2005), sideward translation can be separated from yaw rotationbecause of the different frequency content of the self-motioncomponents, reflected in the relatively high coherence in ad-jacent frequency bands. Therefore all six cardinal axes ofself-motion can be read out in a relatively simple way from thepopulation response of VS and HS neurons. Furthermore,combining responses of different neurons may reduce ambigu-ities arising from the neuronal variability in the responses ofVS and HS neurons (e.g., Haag and Borst 2004; Warzecha andEgelhaaf 2001; Warzecha et al. 2003; Zohary et al. 1994).

Although specific representations of all six self-motion pa-rameters are obtained by combining signals of various sub-populations of VS and HS neurons in a linear way, it is likelythat combining responses in a more sophisticated way may leadto even more specific neuronal representations of self-motion.All schemes proposed can be considered as feasibility proofs,revealing that the population response of VS and HS neurons

contains behaviorally relevant information that can be ex-tracted in well-defined ways. Other decoding schemes maywell be realized in the real system. This limitation pertains tomost systems where neuronal population activity has beenanalyzed and for most computational mechanisms suggestedfor decoding neuronal population responses (for review seeDayan and Abbott 2001; Pouget et al. 2003). Hitherto there areonly few neuronal systems where the decoding of sensorypopulation activity by downstream motor systems has beeninvestigated. One example is the mechanosensory system ofthe leech controlling evasive bending movements of the animal(e.g., Garcia-Perez et al. 2005; Lewis and Kristan 1998; Zoc-colan and Torre 2002; Zoccolan et al. 2002). There are alsoinitial attempts to analyze how the population response of VSand HS neurons is decoded to control compensatory headmovements (Huston and Krapp 2003). In addition, modelsimulations are used to test how HS neurons may steer asaccadic controller, allowing a model fly to navigate in com-plex environments (Lindemann et al., unpublished observa-tions). Moreover, we could show in a recent study that the axisof self-rotation can be inferred by a Bayesian decoder (forreview see Dayan and Abbott 2001) from the populationresponse of VS neurons (Karmeier et al. 2005). It would beinteresting to extend this analysis to population responsesevoked by naturalistic optic flow stimuli.

In conclusion, the responses of output neurons of the blow-fly’s visual motion pathway are largely shaped by the specificdynamical properties of the fly’s saccadic flight and gazestrategy. This strategy has been interpreted as a simple way tosqueeze most of the rotational optic flow into saccades, leadingto optic flow between saccades that contains a strong transla-tional component (Kern et al. 2005). This is likely to bedecisive from a functional perspective because only the trans-lational optic flow component contains information about thespatial layout of the environment. To blowflies, optic flow ismost likely the only relevant source of information about thespatial layout of the outside world. A large part of the outputneurons of the blowfly’s visual motion pathway thus seems to

FIG. 6. Population coding of self-motion: neuro-nal populations appropriate for the encoding of self-motion around and along all 3 cardinal head axes.A–C: specificity to self-rotation is enhanced by sub-tracting the responses of 2 sets of neurons fromopposite sides of the visual sphere having the samepreferred rotation axis but opposite preferred rota-tion directions. A: subtracting responses of a groupof heterolateral VS neurons with laterally locatedreceptive fields increases the specificity to roll rota-tion. B: subtracting responses of heterolateral HSneuron pairs (HSN, HSE, and HSS) increases thespecificity to yaw rotation. C: subtracting responsesof VS neurons with frontally and caudally locatedreceptive fields should increase the specificity topitch rotation. D–F: specificity to self-translation isenhanced by summating responses of neurons ex-hibiting the same sensitivity or by subtracting neu-rons with opposite sensitivity to the respective self-motion. D: summating responses of all recorded VSneuron types enhances the specificity to up-/down-ward translation. E: summating responses of hetero-lateral HSS neurons with ventrally located receptivefields increases the specificity to forward translation.F: subtracting responses of heterolateral HS neuronpairs (HSN, HSE, and HSS) increases the specificityto sideward translation.



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be well adapted to extract behaviorally relevant informationfrom optic flow.

G R A N T S

This work was supported by the Deutsche Forschungsgemeinschaft.

R E F E R E N C E S

Averbeck BB and Lee D. Coding and transmission of information by neuralensembles. Trends Neurosci 27: 225–230, 2004.

Bair W and O’Keefe LP. The influence of fixational eye movements on theresponse of neurons in area MT of the macaque. Vis Neurosci 15: 779–786,1998.

Becker W. Saccades. In: Eye Movements, edited by Carpenter RHS. London:Macmillan, 1992, p. 95–137.

Bendat JS and Piersol AG. Random Data. New York: Wiley–Interscience,2000.

Boeddeker N, Lindemann JP, Egelhaaf M, and Zeil J. Responses of blowflymotion-sensitive neurons to reconstructed optic flow along outdoor flightpaths. J Comp Physiol A Neuroethol Sens Neural Behav Physiol 191:1143–1155, 2005.

Borst A and Haag J. Neural networks in the cockpit of the fly. J CompPhysiol A Sens Neural Behav Physiol 188: 419–437, 2002.

Burr D. Eye movements: keeping vision stable. Curr Biol 14: R195–R197,2004.

Carpenter RHS. Movements of the Eyes. London: Pion, 1988.Dahmen HJ, Franz MO, and Krapp HG. Extracting egomotion from optic

flow: limits of accuracy and neural matched filters. In: Computational,Neural and Ecological Constraints of Visual Motion Processing, edited byZanker JM and Zeil J. Berlin: Springer-Verlag, 2000.

David SV, Vinje WE, and Gallant JL. Natural stimulus statistics alter thereceptive field structure of V1 neurons. J Neurosci 24: 6991–7006, 2004.

Dayan P and Abbott LF. Theoretical Neuroscience: Computational andMathematical Modeling of Neural Systems. Cambridge, MA: MIT Press,2001.

Deadwyler SA and Hampson RE. The significance of neural ensemble codesduring behavior and cognition. Annu Rev Neurosci 20: 217–244, 1997.

Dror RO, O’Carroll DC, and Laughlin SB. Accuracy of velocity estimationby Reichardt correlators. J Opt Soc Am A Opt Image Sci Vis 18: 241–252,2001.

Egelhaaf M, Grewe J, Karmeier K, Kern R, Kurtz R, and Warzecha A.Novel approaches to visual information processing in insects: case studieson neuronal computations in the blowfly visual motion pathway. In: Meth-ods in Insect Sensory Neuroscience, edited by Christensen T. Boca Raton,FL: CRC Press, 2004.

Egelhaaf M, Kern R, Krapp HG, Kretzberg J, Kurtz R, and WarzechaAK. Neural encoding of behaviourally relevant visual-motion information inthe fly. Trends Neurosci 25: 96–102, 2002.

Egelhaaf M and Reichardt W. Dynamic response properties of movementdetectors: theoretical analysis and electrophysiological investigation in thevisual system of the fly. Biol Cybern 56: 69–87, 1987.

Farrow K, Borst A, and Haag J. Sharing receptive fields with your neigh-bors: tuning the vertical system cells to wide field motion. J Neurosci 25:3985–3993, 2005.

Fitzpatrick DC, Batra R, Stanford TR, and Kuwada S. A neuronalpopulation code for sound localization. Nature 388: 871–874, 1997.

Franceschini N. Sampling of Visual Environment by the Compound Eye of theFly: Fundamentals and Applications. Berlin: Springer-Verlag, 1975.

Garcia-Perez E, Mazzoni A, Zoccolan D, Robinson HPC, and Torre V.Statistics of decision making in the leech. J Neurosci 25: 2597–2608, 2005.

Georgopoulos AP, Schwartz AB, and Kettner RE. Neuronal populationcoding of movement direction. Science 233: 1416–1419, 1986.

Groh JM. Predicting perception from population codes. Nat Neurosci 3:201–202, 2000.

Haag J and Borst A. Encoding of visual motion information and reliability inspiking and graded potential neurons. J Neurosci 17: 4809–4819, 1997.

Haag J and Borst A. Active membrane properties and signal encoding ingraded potential neurons. J Neurosci 18: 7972–7986, 1998.

Haag J and Borst A. Recurrent network interactions underlying flow-fieldselectivity of visual interneurons. J Neurosci 21: 5685–5692, 2001.

Haag J and Borst A. Neural mechanism underlying complex receptive fieldproperties of motion-sensitive interneurons. Nat Neurosci 7: 628–634,2004.

Hausen K. Functional characterization and anatomical identification of motionsensitive neurons in the lobula plate of the blowfly Calliphora erythro-cephala. Z Naturforsch 31c: 629–633, 1976.

Hausen K. Monocular and binocular computation of motion in the lobula plateof the fly. Verh Dtsch Zool Ges 74: 49–70, 1981.

Hausen K. Motion sensitive interneurons in the optomotor system of the fly.I. The horizontal cells: structure and signals. Biol Cybern 45: 143–156,1982a.

Hausen K. Motion sensitive interneuron in the optomotor system of the fly. II.The horizontal cells: receptive field organization and response characteris-tics. Biol Cybern 46: 67–79, 1982b.

Hengstenberg R. Common visual response properties of giant vertical cells inthe lobula plate of the blowfly Calliphora. J Comp Physiol A Sens NeuralBehav Physiol 149: 179–193, 1982.

Hengstenberg R, Hausen K, and Hengstenberg B. The number and structureof giant vertical cells (VS) in the lobula plate of the blowfly Calliphoraerythrocephala. J Comp Physiol A Sens Neural Behav Physiol 149: 163–177,1982.

Horstmann W, Egelhaaf M, and Warzecha AK. Synaptic interactionsincrease optic flow specificity. Eur J Neurosci 12: 2157–2165, 2000.

Huston S and Krapp HG. The visual receptive field of a fly neck motorneuron. In: Proceedings of the 29th Gottingen Neurobiology Conference,edited by N. Elsner and Zimmermann H. New York: Thieme, 2003.

Johnston D and Wu MS. Foundations of Cellular Neurophysiology Cam-bridge, MA: MIT Press, 1995.

Karmeier K, Krapp HG, and Egelhaaf M. Robustness of the tuning of flyvisual interneurons to rotatory optic flow. J Neurophysiol 90: 1626–1634,2003.

Karmeier K, Krapp HG, and Egelhaaf M. Population coding of self-motion:applying bayesian analysis to a population of visual interneurons in the fly.J Neurophysiol 94: 2182–2194, 2005.

Kern R, van Hateren JH, Michaelis C, Lindemann JP, and Egelhaaf M.Function of a fly motion-sensitive neuron matches eye movements duringfree flight. PLoS Biol 3: e171, 2005.

Krapp HG, Hengstenberg B, and Hengstenberg R. Dendritic structure andreceptive-field organization of optic flow processing interneurons in the fly.J Neurophysiol 79: 1902–1917, 1998.

Krapp HG, Hengstenberg R, and Egelhaaf M. Binocular contributions tooptic flow processing in the fly visual system. J Neurophysiol 85: 724–734,2001.

Lee D, Port NL, Kruse W, and Georgopoulos AP. Variability and correlatednoise in the discharge of neurons in motor and parietal areas of the primatecortex. J Neurosci 18: 1161–1170, 1998.

Lewis JE and Kristan WB. A neuronal network for computing populationvectors in the leech. Nature 391: 76–79, 1998.

Lindemann JP, Kern R, Michaelis C, Meyer P, van Hateren JH, andEgelhaaf M. FliMax, a novel stimulus device for panoramic and high-speedpresentation of behaviourally generated optic flow. Vision Res 43: 779–791,2003.

Lindemann JP, Kern R, van Hateren JH, Ritter H, and Egelhaaf M. Onthe computations analyzing natural optic flow: quantitative model analysisof the blowfly motion vision pathway. J Neurosci 25: 6435–6448, 2005.

Nicolelis MA, Ghazanfar AA, Stambaugh CR, Oliveira LM, Laubach M,Chapin JK, Nelson RJ, and Kaas JH. Simultaneous encoding of tactileinformation by three primate cortical areas. Nat Neurosci 1: 621–630, 1998.

Nirenberg S and Latham PE. Population coding in the retina. Curr OpinNeurobiol 8: 488–493, 1998.

Pouget A, Dayan P, and Zemel R. Information processing with populationcodes. Nat Rev Neurosci 1: 125–132, 2000.

Pouget A, Dayan P, and Zemel RS. Inference and computation with popu-lation codes. Annu Rev Neurosci 26: 381–410, 2003.

Reinagel P. How do visual neurons respond in the real world? Curr OpinNeurobiol 11: 437–442, 2001.

Schilstra C and van Hateren JH. Blowfly flight and optic flow. I. Thoraxkinematics and flight dynamics. J Exp Biol 202: 1481–1490, 1999.

Stavenga D, Schwering P, and Tinbergen J. A three-compartment modeldescribing temperature changes in tethered flying blowflies. J Exp Biol 185:326–333, 1993.

Theunissen F, Roddey JC, Stufflebeam S, Clague H, and Miller JP.Information theoretic analysis of dynamical encoding by four identifiedprimary sensory interneurons in the cricket cercal system. J Neurophysiol75: 1345–1364, 1996.

Theunissen FE and Miller JP. Representation of sensory information in thecricket cercal sensory system. II. Information theoretic calculation of system



on May 28, 2008

jn.physiology.orgD

ownloaded from


accuracy and optimal tuning-curve widths of four primary interneurons.J Neurophysiol 66: 1690–1703, 1991.

Thiele A, Henning P, Kubischik M, and Hoffmann K-P. Neural mecha-nisms of saccadic suppression. Science 295: 2460–2462, 2002.

van Hateren JH, Kern R, Schwerdtfeger G, and Egelhaaf M. Function andcoding in the blowfly H1 neuron during naturalistic optic flow. J Neurosci25: 4343–4352, 2005.

van Hateren JH, Ruttiger L, Sun H, and Lee BB. Processing of naturaltemporal stimuli by macaque retinal ganglion cells. J Neurosci 22: 9945–9960, 2002.

van Hateren JH and Schilstra C. Blowfly flight and optic flow. II. Headmovements during flight. J Exp Biol 202: 1491–1500, 1999.

van Hateren JH and Snippe HP. Information theoretical evaluation ofparametric models of gain control in blowfly photoreceptor cells. Vision Res41: 1851–1865, 2001.

Vinje WE and Gallant JL. Natural stimulation of the nonclassical receptivefield increases information transmission efficiency in V1. J Neurosci 22:2904–2915, 2002.

Warzecha A and Egelhaaf M. Neuronal encoding of visual motion inreal-time. In: Motion Vision—Computational, Neural, and Ecological Con-straints, edited by Zeil J and Zanker J. New York: Springer-Verlag, 2001.

Warzecha A, Kurtz R, and Egelhaaf M. Synaptic transfer of dynamic motioninformation between identified neurons in the visual system of the blowfly.Neuroscience 119: 1103–1112, 2003.

Warzecha AK, Egelhaaf M, and Borst A. Neural circuit tuning fly visualinterneurons to motion of small objects. I. Dissection of the circuit bypharmacological and photoinactivation techniques. J Neurophysiol 69: 329–339, 1993.

Zhang K, Ginzburg I, McNaughton BL, and Sejnowski TJ. Interpretingneuronal population activity by reconstruction: unified framework withapplication to hippocampal place cells. J Neurophysiol 79: 1017–1044,1998.

Zoccolan D, Pinato G, and Torre V. Highly variable spike trains underliereproducible sensorimotor responses in the medicinal leech. J Neurosci 22:10790–10800, 2002.

Zoccolan D and Torre V. Using optical flow to characterize sensory-motorinteractions in a segment of the medicinal leech. J Neurosci 22: 2283–2298,2002.

Zohary E, Shadlen MN, and Newsome WT. Correlated neuronal dischargerate and its implications for psychophysical performance. Nature 370:140–143, 1994.



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